%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU548^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 02:43:35 PM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( ( in @ eigen__3 @ eigen__1 )
=> ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( sP1
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__1 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ eigen__1 )
=> ( in @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__3 = eigen__2 )
=> ( ( in @ eigen__3 @ eigen__1 )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( in @ eigen__3 @ eigen__1 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> ( in @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__2 = eigen__3 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__3 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ eigen__0 )
=> ( in @ X2 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__2 = eigen__3 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__1 = eigen__0 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__0 = eigen__1 )
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP23
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(def_inCongP,definition,
inCongP = sP9 ).
thf(in__Cong,conjecture,
( sP9
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP9
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[in__Cong]) ).
thf(h1,assumption,
sP9,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eigen__0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ eigen__0 )
= ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP23
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ eigen__0 )
= ( in @ X2 @ eigen__1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP23,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ eigen__0 )
= ( in @ X2 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( sP1
= ( in @ X1 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP17
=> ( sP1 = sP18 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP17,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1 != sP18,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
sP18,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP11
| ~ sP17
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| ~ sP1
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP14
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP24
| ~ sP23
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h5,h9,h11,h12]) ).
thf(9,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP5
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP19
| ~ sP21
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP6
| ~ sP12
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP7
| ~ sP18
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP22
| ~ sP23
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP15
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP16
| ~ sP17
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP20
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP4
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
sP4,
inference(eq_sym,[status(thm)],[]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h9,h10,h8,h7,h5,h6,h4,h3,h1,h2,h0])],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,h1,h5,h9,h13,h14]) ).
thf(24,plain,
$false,
inference(tab_be,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h4,h3,h1,h2,h0]),tab_be(discharge,[h11,h12]),tab_be(discharge,[h13,h14])],[h10,8,23,h11,h12,h13,h14]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,24,h9,h10]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,25,h8]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,26,h7]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,27,h5,h6]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,28,h4]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,29,h3]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,30,h1,h2]) ).
thf(0,theorem,
( sP9
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU548^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 21:08:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % Mode: mode213
% 0.20/0.38 % Inferences: 10
% 0.20/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------